Translator Disclaimer
29 January 2007 Perspex Machine VIII: axioms of transreal arithmetic
Author Affiliations +
Abstract
Transreal arithmetic is a total arithmetic that contains real arithmetic, but which has no arithmetical exceptions. It allows the specification of the Universal Perspex Machine which unifies geometry with the Turing Machine. Here we axiomatise the algebraic structure of transreal arithmetic so that it provides a total arithmetic on any appropriate set of numbers. This opens up the possibility of specifying a version of floating-point arithmetic that does not have any arithmetical exceptions and in which every number is a first-class citizen. We find that literal numbers in the axioms are distinct. In other words, the axiomatisation does not require special axioms to force non-triviality. It follows that transreal arithmetic must be defined on a set of numbers that contains{-∞,-1,0,1,∞,&pphi;} as a proper subset. We note that the axioms have been shown to be consistent by machine proof.
© (2007) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
James A. D. W. Anderson, Norbert Völker, and Andrew A. Adams "Perspex Machine VIII: axioms of transreal arithmetic", Proc. SPIE 6499, Vision Geometry XV, 649902 (29 January 2007); https://doi.org/10.1117/12.698153
PROCEEDINGS
12 PAGES


SHARE
Advertisement
Advertisement
RELATED CONTENT

Perspex Machine IX: transreal analysis
Proceedings of SPIE (January 28 2007)
The use of a radix 5 base for transmission and...
Proceedings of SPIE (March 07 2008)
A comparison of a Radix 2 and a Radix 5...
Proceedings of SPIE (September 04 2008)
PDF X "Family Tree" a new challenge for Internet...
Proceedings of SPIE (December 19 2001)
Give to Get free riding resilient video on demand...
Proceedings of SPIE (January 27 2008)
Multimedia browser (MMB)
Proceedings of SPIE (July 19 2001)

Back to Top